....It seems to me that a better stance would be the old gun-slinger style. Pistol held at waist and close in to your body. Now you can protect your pistol / self with off hand and or body or even obscure your weapon. With a little practice you'll some find that the bullets go where you are looking or close to it without looking at your sights.

Why isn't this taught?

It is -- actually not exactly that way. Current thinking is to engage near targets from what's called the retention position. This is an intermediate step in the standard draw stroke and has the gun held up at about the level of the pectoral muscle and fairly close into the body.

But this is something covered "down the road" in a normal training progression.

The thing is that one needs to start somewhere. Generally a training program begins with the Weaver and/or Isosceles and the two hand grip. The first goal is to lay a solid foundation of the fundamentals -- trigger control and sight alignment.

Then a training program normally progresses to one handed shooting, both dominant hand only and non-dominant hand only, then various forms of point shooting. And throw in some moving targets, moving and shooting, shooting while moving, multiple targets, etc., and you'll be beginning to get some well rounded training.